Introdução ao cálculo variacional e problemas de otimização aplicados no ensino básico
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| Main Author: | |
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| Publication Date: | 2019 |
| Format: | Master thesis |
| Language: | por |
| Source: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/10140 |
Summary: | This study we discuss and solve a series of classic optimization problems linked to variational calculus, with emphasis on brachistochron. Afterwards, there are suggestions of some activities to be developed with middle and high school, focused on the resolution of the basic problems of variational calculus via experiments. We seek to present a variational calculus basis and as its main propositions, with the due mathematical rigor. It briefly discusses the historical development of the variational calculus and it deduces the main equations: the Euler Lagrange Equation and its developments, and the conditions that ensure that a Lagrangian must meet to be the maximum or minimum. |